Abgeschlossene Arbeiten


Gruppen Bluhm DiVincenzo Hassler Müller Terhal



Gruppe Bluhm


  Gekoppelte Qubits Urheberrecht: © Simon Schaal

B.Sc.-Arbeit Long Range
Coupling between Spin Qubits

The Double Quantum Dot system in GaAs can be used for quantum information processing. This thesis benchmarks different ways to couple several qubits to enable good multi-qubit operations.
Dokument (PDF)

  Zentrales Spinproblem Urheberrecht: © Christian Dickel

M.Sc.-Arbeit Nuclear Spin Mediated Landau-Zener Transitions in Double Quantum Dots

The Double Quantum Dot system in GaAs is a promising hardware for quantum information processing. In this thesis, a measurement scheme to probe the dynamics of nuclear spins in GaAs quantum dots is presented. Dokument (PDF)

  Quantengatter Urheberrecht: © Pascal Cerfontaine

M.Sc.-Arbeit High-Fidelity Qubit Gates for Two-Electron Spin Qubits

High-fidelity gate operations for manipulating qubits in the presence of decoherence are a prerequisite for fault-tolerant quantum information processing. This work theoretically develops control pulses for singlet-triplet qubits in GaAs double quantum dots with fidelities as high as 99.9%.
Dokument (PDF)

  Messsequenz Urheberrecht: © Thomas Fink

M.Sc.-Arbeit Probing Classical and Quantum-Mechanical Baths with a Qubit

The investigation of deleterious interactions between a qubit and its environment is important for quantum information research. In this thesis, techniques using qubit evolution and readout to investigate interactions with both classical and quantum-mechanical noise baths are introduced.
Dokument (PDF)



Gruppe DiVincenzo




  Perturbed solution Urheberrecht: © Evangelos Varvelis

M.Sc.-Project Beyond the rotating wave approximation dynamics of high-fidelity quantum gates ​

In this thesis, using the effective Hamiltonian approach based on the Magnus expansion, the time evolution of high-fidelity quantum gate for singlet-triplet qubit is studied. A new approach for calculating such an effective Hamiltonian is presented. The goal of this new methodoloy is to find a non-recursive formula for the effective Hamiltonian, thereby reducing the computational cost of determining such effective Hamiltonians. In the process of doing so, few simplifications are obtained as well as new directions for further development of the formalism is motivated. Thesis

  2 qubit Simon algorithm Urheberrecht: © Rijul Sachdeva

M.Sc.-Project Exploring remote quantum computation using Simon Algorithm within Blind Oracular Quantum Computation scheme ​

In this thesis, the concept of Universal blind quantum computation, in which a client with limited resources controls the execution of a quantum computation on a server without revealing any details of the computation, is developed. This idea is extended to a threenode setup used to carry out oracular quantum computation in a blind environment. In this Blind Oracular Quantum Computation(BOQC) scheme, there is the Oracle, with limited power along with the client to supply quantum information to the server so that the oracular part of the computation can also be carried out blindly. We develop tests of this protocol using Grover and Simon Algorithm. Thesis

  Infinitely squeezed GKP code states Urheberrecht: © Jonathan Conrad

M.Sc.-Project Tailoring GKP Error Correction to Real Noise ​

In the wake of recent experimental advances in high precision control of quantum harmonic oscillators, such as embedded in trapped ions or microwave cavities, the theme of this work is to analyze noise processes a particular bosonic quantum error correcting code, called the GKP-Code, experiences in realistic scenarios, and to investigate how one can adapt decoding strategies to cope for such noise. To this end, this work presents analytical studies of error channels that perturb GKP-encoded qubits, i.e. propagated finite squeezing (finite energy) errors and photon loss. It is shown, how one can use these results to derive tailored decoding strategies, which are then tested in numerical simulations. Furthermore, we discuss how one can implement and use machine-learning techniques to further adapt decoding strategies to hardware. Thesis

  A quantum trajectory Urheberrecht: © Tobias Herrig

M.Sc.-Project Measurement Simulations of Coupled Qubits with QuTiP ​

The motivation for this thesis was to investigate if and how it is possible to realize a single-qubit measurement in a system of coupled qubits. The goal was to simulate a homodyne detection on a system with two coupled qubits and a readout resonator. Thesis

  Hofstaedter Butterfly Urheberrecht: © Martin Rymarz

M.Sc.-Project The Quantum Electrodynamics of Singular and Nonreciprocal Superconducting Circuits

This thesis deals with two systems in the field of circuit quantum electrodynamics. In the first part we extend a recently proposed singular superconducting circuit architecture that realizes a qubit-resonator system with tunable coupling, in particular taming the circuit singularity. In the second part we introduce the gyrator into circuit quantum electrodynamics, discussing its quantization, its potential singularity and how to cancel it, as well as its non-reciprocity, which is furthermore studied with the aid of an example. Thesis

  Concurrence squared as a function of time and detuning. Urheberrecht: © Joel Christin Pommerening

M.Sc.-Project Multiqubit Coupling Dynamics and the Cross-Resonance Gate​

The cross-resonance gate is implemented by applying a microwave drive to a system of two coupled qubits. I study the nonlocal properties of the driven and undriven system induced by this coupling. In the undriven case, entanglement is still being generated, but it is periodic and bounded linearly by the ratio of coupling strength and qubit frequency detuning. Specifically I derive an upper bound for the concur- rence as a measure of entanglement. Dokument(PDF)

  Sketch of QuBus Finite Element Configuration. Urheberrecht: © Veit Langrock

M.Sc.-Project Numerical and theoretical investigation of long-range coherent electron shuttling devices in Silicon/Silicon-Germanium quantum wells for scalable quantum computing ​

The aim of this thesis is to investigate what kind of problems currently envisioned coherent electron transfer devices may encounter in Silicon/Silicon- Germanium gate-confined nano structures, and to lay out proper methods to de- scribe them in a sufficiently efficient manner. Thesis

  Superconducting Qubit GUI initial window. Urheberrecht: © Adrián Parra Rodríguez

M.Sc.-Project Software Tool to Analyse Superconducting Qubits

This thesis is a description of the program “Superconducting Qubit GUI” that following the methods of existing literature, it helps automate ordinary electrical network graph theory in superconducting circuits.The main objective of the Superconducting Qubit GUI is to be as useful as possible to a researcher in the field. It is open to changes for improvement since the written code offers a nice interface for further development. Dokument


M.Sc.-Arbeit Quantum Information Processing with Surface Acoustic Waves ​

Alan Salari

In the first part of the present work, I’m going to investigate the wave propagation in cubic piezoelectric crystals such as GaAs and also wave generation by interdigital transducers. In the second part, I propose and investigate the idea of looking at spiral IDT-like structures, which might permit the simultaneous coupling to two cavities in orthogonal directions. Using COMSOL simulations, I’ve calculated several parameters of the spiral transducer, such as its capacitance, input admittance and response function. The coupling rate of the spiral transducer has also been calculated using semi-classical model for the qubit.Moreover, I have studied the IDT-transmons of Delsing's group. The physics of this is rather different than in conventional "circuit QED", because the transmon capacitor will be much bigger than the wavelength of the bosonic mode, makes it a giant atom. Dokument

  Carlin Plot Urheberrecht: © Sander Konijnenberg

M.Sc.-Arbeit Theoretical study of Hall effect gyrators and circulators in the time domain ​

Circulators and gyrators are non-reciprocal circuit elements that play an important role in microwave systems. It would be desirable to keep such elements small in size, so it has been proposed to create such devices that use the Hall effect (as opposed to e.g. the Faraday effect which makes for relatively large devices). It has been shown that by coupling leads capacitively to a 2D Hall conductor, lossless circulators and gyrators can be made. The response of such devices has been studied in the frequency domain, but these results cannot be trivially transformed to the time domain. In this report we study the behaviour of Hall-effect gyrators and circulators in the time domain. Dokument (PDF)

  Energy of dressed states vs detuning Urheberrecht: © Susanne Richer

M.Sc.-Arbeit Perturbative Analysis of Two-Qubit Gates on Transmon Qubits

This thesis treats different schemes for two-qubit gates on transmon qubits and their per- turbative analysis. The transmon qubit is a superconducting qubit that stands out due to its very low sensitivity to charge noise, leading to high coherence times. However, it is also characterized by its low anharmonicity, making it impossible to neglect the higher transmon levels.

Coupled systems of superconducting qubits and resonators can be treated in cavity QED. In the dispersive regime, where qubit and resonator are far detuned from each other, per- turbative methods can be used for the derivation of effective Hamiltonians. Several such methods are presented here, among which the Schrieffer-Wolff transformation results to be the most adequate. Dokument (PDF)


Gruppe Hassler




      Honeycomb Majorana lattice Urheberrecht: © Anton Montag

    Hexagonal Majorana fermion lattice constructed from topological insulator Josephson junctions

    In this thesis, we discuss the realization of a hexagonal Majorana fermion lattice and its thermal transport properties. We analyze the two-dimensional Josephson junctions on the surface of topological insulators to obtain topological Majorana wires in the low-energy regime. Using this description of the wires, we construct trijunctions and derive three distinct topological phases of them, two of which host Majorana bound states. We connect multiple Majorana bound states with topological insulator Josephson junctions to a hexagonal lattice of Majorana fermions. The spectrum of this lattice is calculated, the appearance of edge states is shown, and the scaling behavior of the thermal conductance of the hexagonal Majorana lattice is analyzed. Dokument (PDF)

      Spectrum of Lindblad equation Urheberrecht: © Steven Kim

    Lindblad Equation, Symmetries, and Instabilities in Driven-Dissipative Systems

    In this thesis, we study driven-dissipative systems that can be de- scribed by a Lindblad master equation. In particular, we analyze parametrically driven oscillators that exhibit an instability when the driving strength exceeds the damping. In this critical regime, both fluctuations and nonlinearities have to be included for an accurate description of the system. For the degenerate parametric oscilla- tor, it has been shown that the long-time dynamics can be described by a universal Liouvillian. This makes the efficient calculation of observables, such as the photon current, possible. To determine the long-time dynamics, we provide a method to solve the Lindblad equation, which makes the separation of timescales possible. This is used to derive the effective model for the non-degenerate parametric os- cillator, and we analyze the resulting statistics of radiation. Additionally, we discuss how symmetries of the Lindblad equation are described. Dokument (PDF)

      Majorana toric code Urheberrecht: © Alexander Ziesen

    Lattice Gauge Theoretic Analysis of Topological Ordering in the Majorana Toric Code

    In this thesis, we consider a two dimensional square lattice of mesoscopic superconducting islands carrying four Majorana zero modes (MZM) each. We consider the islands to form an array of Josephson junctions, where the MZM allow for additional inter-island single electron transfer. This model is known to realize topological order in the form of Kitaev's toric code. With a calculation of the effective Hamiltonian, we prove that the presence of charge-2e Josephson tunneling has a stabilizing effect on the toric code gap. The goal of this thesis is to investigate the signatures of topological ordering. To this end, we introduce a duality mapping of the MZM to spins yielding a lattice gauge theory and shift the focus from the matter to the gauge perspective. In this form, we can utilize the equal time formulation of the Fredenhagen-Marcu order parameter, a generalized Wilson loop, to detect the topological signatures and give an intuitive picture of (open) loop condensation to understand the topological phase
    transition. Dokument (PDF)

      circuit for dual shapiro step Urheberrecht: © Lisa Arndt

    Dual Shapiro steps of a phase-slip junction in the presence of a parasitic capacitance

    This thesis investigates the emergence of dual Shapiro steps in the IV-curve of a single Josephson junction in the phase-slip regime. In particular, we analyze the detrimental effect of the parasitic capacitance between the biasing lines and how it can be remedied by an on-chip superinductance. We obtain an explicit analytical expression for the height of dual Shapiro steps as a function of the ratio of the parasitic capacitance to the superinductance. Using this result, we provide a quantitative estimate of the dual Shapiro step height. Our calculations reveal that even in the presence of a parasitic capacitance it should be possible to observe dual Shapiro steps with realistic experimental parameters. Dokument (PDF)

      Algebraic Methods for the 1D Schrödinger Equation Urheberrecht: © Florian Venn

    Algebraic Methods for the 1D Schrödinger Equation

    We discuss algebraic methods to obtain exact results about the eigenvalue spectrum of the one dimensional Schrödinger equation. We focus on degeneracies in the spectrum and eigenvalues that are exactly solvable. The central object in our discussion is supersymmetry. First, we give an introduction to the description of problems using superpotentials. We present insights that can be obtained from the supersymmetric structure, in particular the degeneracies between bosonic and fermionic states and that the groundstate admits an algebraic solution. We use these insights to study the double sine potential. By tuning the double sine potential away from the point where it can be described using supersymmetry, we find an extension of supersymmetry that is related to a class of problems for which multiple eigenstates admit algebraic solutions. Next, we prove, for a subclass of these problems, that a degenerate partner state exists for almost all eigenstates. Finally, we highlight that the class of periodic problems with more than one exactly solvable eigenvalue is not limited to the double sine potential. Dokument (PDF)

      Edge scattering at a graphene boundary Urheberrecht: © Elias Walter

    Influence of chiral symmetry on electron scattering at disordered graphene boundaries

    In this thesis, we study scattering processes at disordered graphene boundaries. In particular, we investigate how the chiral symmetry of quasiparticles in graphene influences diffusive scattering. We find that a boundary that breaks chiral symmetry behaves like a mirror, in the sense that in the long Fermi wavelength limit diffusive scattering is suppressed and incoming electrons are reflected specularly. However, if the disorder on average preserves chiral symmetry, diffusive scattering increases significantly, leading to a breakdown of the mirror-like behavior. Dokument (PDF)

      Setup photons from QPC Urheberrecht: © Daniel Otten

    Second-Order Coherence of Microwave Photons Emitted by a Quantum Point Contact

    In this work we present a diagrammatic approach to calculate current cumulants for the electron transport through a quantum point contact. We provide compact expressions for cumulants up to and including the third order. Furthermore, fluctuations in the electronic current lead to emitted radiation in the microwave regime. In this context the current cumulants are linked to the photon counting statistics of the microwave field. For this setup, we calculate the Fano factor F and the second-order coherence function g (2)(τ). Dokument (PDF)

      Aharonov-Bohm interference ring Urheberrecht: © Dominique Dresen

    Quantum Transport of Non-Interacting Electrons in 2D Systems of Arbitrary Geometries

    The scattering formalism for describing the trans p ort properties of systems is discussed. We apply the formalism to GaAs and graphene with different geometries and types of disorder. For example, we discuss impedance matching of graphene to outside leads, Aharnnov-Bohm effect in a ring geometry, and how strain-fluctuations in graphene manifest themselves in the transport properties. Dokument (PDF)

      elektrische Schaltung Urheberrecht: © Sebastian Rubbert

    Tuneable Long Range Interactions in an Array of coupled Cooper Pair Boxes

    The Kitaev chain emulating the transverse Ising model can be implemented in an array of superconducting islands with semiconducting nanowires. In this thesis, we will show that adding additional capacitances to the system implements a long-range interaction between the Ising degrees of freedom. Dokument (PDF)





    Gruppe Müller






    Gruppe Terhal




      Code state Urheberrecht: © Daniel Weigand

    M.Sc. Project Deterministic Encoding of a Qubit in a Cavity Mode using Phase Estimation

    In this thesis, several deterministic protocols are proposed and analyzed that use circuit quantum electrodynamics to approximately encode a qubit in an oscillator by dispersively coupling a transmon qubit to a microwave cavity mode.

    Thesis (PDF)

      Code state Urheberrecht: © Yang Wang

    M.Sc. Project Quantum Error Correction with the GKP code and Concatenation with stabilizer codes

    In this thesis, we propose a method to utilize all the information contained in the continuous shifts for quantum error correction, which improves over simply mapping a GKP-encoded qubit to a normal qubit.

    Thesis (PDF)

      Eindimensionaler  Schaltkreis Urheberrecht: © Nikolas Breuckmann

    M.Sc. Project From quantum circuits to Hamiltonians: analysis of a multi-time construction for QMA

    This thesis lies in the area of quantum complexity theory. It proves the QMA-completeness of a class of 2D interacting fermion Hamiltonians.
    Dokument (PDF)

      squeezing Urheberrecht: © Eva Kreysing

    M.Sc. Project Improving Transmon Qubit Readout Using Squeezed Radiation

    The goal of this project has been to analyze whether the use of squeezing in a Mach-Zehnder interferometer can give rise to a faster, high fidelity, measurement of superconducting transmon qubits.
    Dokument (PDF)